Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-20T05:00:07.357Z Has data issue: false hasContentIssue false

Some results about Markov processes on subsets of the state space

Published online by Cambridge University Press:  01 July 2016

Cristina Gzyl*
Affiliation:
Universidad Central de Venezuela

Abstract

Kingman [5] proved a formula that expresses the joint distribution of the processes where b is a regular point in the state space of a Hunt process. We give an extension of this formula, as well as several interesting facts related to it, for the case when Φ is any finely perfect subset of the state space. We also establish some connections between this result and results on last-exit decompositions.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Blumenthal, R. M. and Getoor, R. K. (1968) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
[2] Kingman, J. F. C. (1975) Anticipation processes. In Perspectives in Probability and Statistics, ed. Gani, J. Applied Probability Trust: distributed by Academic Press, London. 201215.Google Scholar
[3] Getoor, R. K. and Sharpe, M. J. (1973) Last exit decompositions and distributions. Indiana Univ. Math. J. 23, 377404.Google Scholar
[4] Getoor, R. K. (1976) On the construction of kernels. In Springer-Verlag Lecture Notes in Mathematics 465, 443463.Google Scholar
[5] Kingman, J. F. C. (1973) Homecomings of Markov processes. Adv. Appl. Prob. 5, 66102.Google Scholar
[6] Getoor, R. K. (1974) Some remarks on a paper of Kingman. Adv. Appl. Prob. 6, 757767.Google Scholar
[7] Getoor, R. K. (1966) Continuous additive functionals of a Markov process with applications to processes with independent increments. J. Math. Anal. 13, 132153.Google Scholar
[8] Meyer, P. A. (1966) Probability and Potentials. Ginn, Boston.Google Scholar
[9] Meyer, P. A. (1967) Lecture Notes No. 26. Springer Verlag, Berlin.Google Scholar
[10] Stone, M. H. (1962) A generalized Weierstrass approximation theorem. Studies in Mathematics, Vol. 1. M.A.A. Prentice-Hall, Englewood Cliffs, N. J. Google Scholar